Need Help On Written Optimization Analysis

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This assignment requires you to analyze and solve an optimization problem presented in an e-mail style format. Download the attached Optimization word problem and read through the scenario. Additional notes have been included within each problem.After you have analyzed the scenario, solve the optimization problems. You will solve the problems using graphical and computational methods. Directions on required resources are available at the bottom.Include a graph along with your solution for problem 1.Include the results from Excel spreadsheet with the values clearly labeled for problem 2.(These can be included within the written response, or as separate files)Then draft a response to the questions posed in each problem. NOTE: Write your response in a professional manner, as if submitting your analysis to a supervisor. Submit your completed analysis in this assignment.————————————-There are a few ways in which you can generate a graph.1)Grapher application in the Utilities folder (within the Applications folder)2)Download the free, open source, dynamic mathematical software Geogebra available at: 

http://www.geogebra.org/

You may either download and use one of the blank templates, or create your own. The included ones match the template in the explanation from the above website.

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Introduction
 

The
 state
 has
 created
 new
 legislation
 about
 “crunch-­‐time”,
 and
 as
 such
 requires
 us
 to
 adjust
 our
 
projects
 for
 the
 next
 quarter.
 
 
 So
 for
 the
 next
 13
 weeks
 we
 will
 assume
 that
 there
 will
 be
 no
 scheduled
 
overtime.
 
 
 Our
 adjusted
 budget
 for
 the
 quarter
 gives
 us
 520
 hours
 per
 employee,
 and
 no
 overtime.
 
 
 So
 
we
 will
 have
 to
 determine
 how
 many
 projects
 we
 can
 complete
 with
 these
 new
 constraints,
 making
 
adjustments
 based
 on
 the
 man-­‐hours
 worked
 on
 previous
 projects.
 
 
 Please
 figure
 out
 the
 number
 of
 
game
 we
 can
 make
 of
 each
 type
 that
 yields
 the
 highest
 profit
 

Note:
 To
 convert
 from
 man-­‐hours
 to
 number
 of
 people,
 divide
 the
 number
 of
 man-­‐hours
 by
 520
 hours
 
(which
 is
 the
 number
 of
 full
 time
 hours
 in
 the
 quarter)
 

Problem
 1
 

To
 create
 a
 console
 game,
 we
 previously
 required
 10,920
 man-­‐hours
 of
 development,
 13,000
 man-­‐hours
 
on
 art,
 3,120
 man-­‐hours
 for
 design,
 and
 2,080
 man-­‐hours
 for
 production
 management.
 
 
 The
 projected
 
profit
 margin
 for
 a
 console
 game
 title
 is
 $1.8
 million.
 

The
 work
 requirements
 for
 a
 handheld
 game
 quite
 a
 bit
 different:
 
 7,280
 man-­‐hours
 in
 development,
 
2,600
 man-­‐hours
 art,
 9,360man-­‐hours
 in
 design,
 and
 2,600
 man-­‐hours
 in
 production
 management.
 The
 
projected
 profit
 margin
 for
 a
 handheld
 game
 title
 is
 $1
 million.
 

Our
 current
 staff
 consists
 of
 238
 programmers,
 225
 artists,
 180
 designers,
 and
 57
 production
 managers.
 
 
 
This
 should
 give
 us
 123,760
 man-­‐hours
 in
 the
 development
 pool
 (238
 x
 520
 =
 123,760),
 
 117,000
 man-­‐
hours
 in
 the
 art
 pool
 (225
 x
 520
 =
 117,000),
 93,600
 man-­‐hours
 in
 the
 design
 pool
 (180
 x
 520
 =
 93,600),
 
and
 29,640
 man-­‐hours
 in
 management
 (57
 x
 520
 =
 29,640)
 to
 allocate
 to
 projects,
 

Figure
 out
 how
 many
 console
 and
 handheld
 games
 can
 be
 made
 this
 quarter
 to
 maximize
 our
 profit.
 
 
 
In
 addition,
 report
 what
 pools
 (development,
 artists,
 designers,
 and
 managers)
 have
 some
 unutilized
 
employees,
 and
 which
 pools
 need
 to
 be
 expanded.
 

Problem
 2
 

We
 have
 decided
 to
 expand
 and
 create
 a
 new
 PC
 games
 department.
 
 
 Out
 projections
 indicate
 PC
 game
 
 
titles
 will
 make
 $1.4
 million
 in
 profit.
 
 
 The
 work
 requirements
 are
 9,360
 man-­‐hours
 for
 development,
 
8,840
 man-­‐hours
 on
 artwork,
 5,720
 man-­‐hours
 for
 design,
 and
 1,560
 man-­‐hours
 for
 production
 
management.
 

To
 help
 staff
 this
 department,
 we
 hired
 44
 more
 programmers
 for
 the
 development
 team,
 58
 more
 
artists
 for
 the
 art
 team,
 and
 2
 more
 managers
 for
 the
 management
 team.
 
 
 Please
 adjust
 the
 total
 man-­‐
hours
 available
 based
 on
 this
 new
 staff
 before
 calculating
 the
 new
 estimations.
 

Figure
 out
 how
 many
 console,
 PC,
 and
 handheld
 games
 can
 be
 made
 this
 quarter
 to
 maximize
 our
 
profit.
 
 
 In
 addition,
 report
 what
 pools
 (development,
 artists,
 designers,
 and
 managers)
 have
 some
 
unutilized
 employees,
 and
 which
 pools
 need
 to
 be
 expanded.
 

Sheet1

Constraint 1

≤ Constraint 2

≤ Constraint 3

X1 X2
Problem Name
Variables X1 X2 Sign RHS LHS Slack
Objective Function = Max P Profit
Constraint 1
Constraint 2
Constraint 3
Solutions

Sheet2

Sheet3

Sheet1

Constraint 1

≤ Constraint 2

≤ Constraint 3

X1 X2 X3
Problem Name
Variables X1 X2 X3 Sign RHS LHS Slack
Objective Function = Max P Profit
Constraint 1
Constraint 2
Constraint 3
Solutions

Sheet2

Sheet3

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